P A L A C E P IE R, S T. L E O N A R D S. R a n n o w, q u a r r y. W WALTER CR O TC H, Esq., Local Chairman. E. CO O PER EVANS, Esq.,.

Size: px
Start display at page:

Download "P A L A C E P IE R, S T. L E O N A R D S. R a n n o w, q u a r r y. W WALTER CR O TC H, Esq., Local Chairman. E. CO O PER EVANS, Esq.,."

Transcription

1 ? ( # [ ( 8? [ > 3 Q [ ««> » 9 Q { «33 Q> 8 \ \ 3 3 3> Q»«9 Q «««<» X 3 3» > 3 <8 3 > X \ [ 3 ( ( Z ( Z 3( 9 9 > < < > >? 8 98 ««3 ( 98 < <» 9 9X8? 8 3? (»> # # Q 3 98? 98 > > ««««> 3 «> [ 98 3 Q 83«3 ( } \< 3? «« \ > 8 < (? 9 ( X»»? \\? > >\ 3> X < ( > ( > }< > \» \ ( ( Q 93»«\ $» X 3 X «z <»» ««8 83 «(> «8 «< Q X X (» 8 9 » > ( «[ 8 8 ± ( ««««X z 8 «> «8 Q ««> < «8» 83 X «9 X «9 «> Z X % «9 «8««Q X X X 3 > ««> X X » > # X X 8 \ 9 ( «> 9 «<«(? «> «\3 8 > 3 3 \ \ X <? X 3 X X 8 «> 9 X \»»» 8 X X 8 8 (> \( <? «> «( > ««\ 39 <»»<8 >?» < «( Q» ««««««% X»Z % X X Q ««? %» ( 8 8 «> 8«»» «z «« ««< X» 8 \ «{ > <»? » 3» ( >X ( X > (}? }» {««X9X? «« $»? Q X » z «?< «#»» 3?\» [ (? ( ««3««3 8 { 8 «««( > > X 3 8 Q < ««««( ( ( >>»» } \ «( 8 \ ( < 3 = # 3 < \»«}» ( 8 ««««9 > «(«9 «X 3 3 «? X «? 3 <} ~? Z» > X «3» 3»«( }\ > 8 <» ««Q33?» 3?» ««# «>? «(»»«X» > Q «X ( <? (? > < (» 8» ~ ( ««( ( >? (< 3 > <»» ( }? > ( \ } ( \» ««\ \\ > \ [{ \ \[ «?? \3 %»\ «> 3» Q «83 X X «% > «< > «3 98»» «# <> > [?»»?» [ 3+ 9? < 9 9 «[ X «> X 3? 9?#3 zz ( Q (? = Q ( ZZ 8 ( ( «98 ( ( ( ( 9 Q ( X [ 3 # ««( 8 (» «# ( 3 ( 98 X X X 3 ( 3 3» «? 9 ( «3 ( «8 3 «X z Z 3? «\ (» 3 39 > [Q 9 ( X» 98 < # [ 8 # ( [ 3 «8 ««Q 8««(% [ > ~ « z 3 «3 >» X Z X 9 ««3 9 < z > 3 > % ««[ «<\ ( < <» $»? 9 <» \ > > 9 ««9$ 8 9 [ 8 9 zz z{ 3 9 ( # { 3 9< < (8?? 98»( 9 QX3 «8% «#» z «\ Q? 83 <

2 Q > ( < >?#»8 «( 3 X»» 9 Q # ««8 98 ( X ( «8 98 [ 38 «> 98 < < 98 Q» Z 98»> $ 3 Q < 9 [ X 3 » 3 98 < <? «<» ««\ 39? ( < \ 9 #» 9 \ \ { 3 9 Z 9 \ «Q > «9» «= «? 9? 98 3 $ X «9$ [ 8 9? zz z 3» > [ 8 # 3 Q8 98» ? Z 3 8 «( 3 ( ( «( > Z 3 [ 3 = = Q ( } < ( (»» ( ( Q ( 8 «3 Q «? 3 > 8 [ X > X \ [? 3 ( X % X 8 Q 3 (3? > 3 98 «\ 3???\\ ( ( < «< X z 3 8 ««= 8 «? ( 3 «z Q «3 3? X? «?? <»«9Q 83»? z ( (? # % < \ \ ( «Q ~ 3 «z z» 3 ~ > < 3< (»» «( <( Z 9 «3? \ }> 8 Q > <» «< z «[ >\?» «3 ««« Q? Q } 3 ( \ ( 8 > z « \» X 9 9 z 3 8 ( ( X > (»» \ z >» > <»? \> 9 3 8< > ( 3» % X «X Z «8 Q X»» X « 33 \ X 3«> «8 # 3 ( «>»» «3 «? >? \ X \ 3 X 3 < < 8« \ \\ 8 9 X?»» Z «\\ Q > > Q Q 8 Q» ( ( (? <\ (? \ \ ( ( > ( 83 3 X» \ \ X? 3 ( ( 3 ( 3 ( ( \ < > ( [ \ ( ( \ ( ( ( X? X X»( # $ <«zz > ««8»\ X \ ( ( X > { 3 33 «\ ZZ 8 X X ( 8 98?»» 9 #»8«[ «? ««« 3 ( «$ Q (> > 98 X X 8[ 3 ( \ zz «>«? }<> «( 3> 3 > > > > > 33 8 > ( ( Q \? «««93»» > ( [ ( Z 3» «( 9 ( ««X? > Z Q X 3 8» [Q 3 8 z \? 3» $ X \ Q# X Q 3 Q «8 3 8 > { 3 Q 8 «z [ z Q ~ <% 3 9 3»> \ «9«< z ( 3 [ 3 «X Z «8 «< Q 3 3 «9 «z Q> ««X \\»? 3 > > > # Q 9 Q «? 3 33 Q »» <> ><«3 >3 «XX X > 9 % «X 38 8 ( (? \ 8

3 = = ««< «3>? #«?? >» >} #>»» > X»\ \ \ %??<> < \?>» \ < #»»»? <» »# ««>» X»< + (? «? «z > Q» < Q Q \ % \ > ««Q< ««( z X «X «8 3 > 9» X {? (> < >? X \ } ( \ > 3 (? \ ( X (»? 8 > X ( > ( \ «( \ ( ( (> ( > < ( < < z \ ( ( ( \» \ 8 < (? ( ( 8 ( 9 ( { \ < \ 3 ( ( \ ( < ( 3 ( \ (? ( < ( ( ~ ( X ( ( (» ( \ \ 3 X\ ( 3 33 X = 3? ( (< ( z 9 9 ( { X 3 3 < < (? «8 ( 8 3? ( ( ( ( Q ( ( { 9 ( \? ( 8 ( Q ( > ««\ 98 % «( ( ( «{ ( «8 «( > > ( > = ( ( (» ( > ( >? > ( 8»<»? ( (» ««««? ( 98 >> Z >? >«( \\ >»? ( \} Z < \( > ( 8 > 3 3 = 3 3 \\ # > 3 [ ( 8 ( X > (? ( 9 ( \ ( ( < ( (> < < \ X 98 ( \ ( (( Q \ ( \» ( } >» < ( ( > ( >? > \\ ( \\ \ > \ \\ > ( > \ ( ( «# 8 X X < 3

4 [ 8 [ $ ( X X Q \} 9 > ( «<=««{ (» X \ 3 9 X ( \ > X z X ( Q = 98 3 ( ( ( Q ( ( 9 ( ( 8 9 X (» ( 3 ( 98? < ( 3 «3 3? 3 3 ( ( X ( ( 98 X X 98 \ 8 [ ( X 3 ( ( 98 ( X 3 ( 9 3 ( Z ( ( 9 X \ ( Q ( «~ ( ( ( 8 ( \ ( \\ \ < X < \\ < > > 8 3> \ ( 8» < { ( «8 # > \ \ «3 { 3 3 > 3 # X «$ 3 ( 8 ««« ( «$ > [ ( «z 8 8 8? = > Z 3 9 (> > 9 « Z X 88 8 X 98 > » > 8 9 \ ( 3 3 \ \ ( [ > 3 « ( [ < \ 83 Q 8 Q } ( ( «X z z 3» 3 ( [ 3 # 8? z ( X 3 X X ( \ 8 ( ? 8 8? ( 3 <» ( > X» >? «3 z «{ 3 ( ( 3 [ #» 3 3 \\ 8 9 ( Q 88 8 ( 3» «# 3 ( [ 3? 98 \ 3 3 <» [ «(» 3 \ ( ( \ ( z > 3 «? 3 < { 9 3 3» <> [ ( (» >?? ( «(< \ ( ( ( 3 < ( ( ( \» > <» ( Q z z? > \ ( <»?? = < «(> \[( \»?»»«> «( ( ( < < [(» 3 3 z \ 3 X \? \ [? ( (»? > ( > X> X 8»? 3 X?? ««8 \( ( X ( ««9 3 «z z 3 3 Q«( > Q < ( \ ( \ \ \ \? \\( ( ( \ < < «( \ \ \ \ \ ( \ 9 < ( ( (? 8 «[ X X \ \ 9 9 ( ( >\ ± ( <[ ( \ ( \ \ [ \ \ ( ( (»«> «\ \ ( \ ( \ ( \ 8 ( 3 \ \ > > (( \> < < ( 8 >9

5 » # > X 9 8 z ( < 8 3 z } [ ( ( 8 ( > ( { ( Q ( z ( z 3 z (? ( (? < (?? > (> ( ( ( ( ( ( ( ( ( ( ( < ( 9 98 ( 89 ( 9 9 z ( ( ( ( ( 8» 3 X? ? <89 ( \ (? 8 z (? ( z X (? 83 8 ( Z Z ( [ ( ( ( 3 ( X ( ( (? z z z [ # zz z X???» ( <? ( ( ( ( z» 98 ( ( 3 [ «3 9 3 ( 3 ( 9 ( z \ (?? (3 39 [ 9 9? ( ( ( ( ( ( 9 8 ( ( [?? < ( ( \ 3 ( 3 89 ( 39 < 3 [ 8 9 Q z ( 88 X 8 3 Q < 9 ( ( < \ Q ( \ ( ( 3 ( ( («(? (8 ± ( 8 3 ( ( X > ( ( 3 3 < z ( ( ( } 3 \ 3 X «( X 3 ( Q ( 3 zz [ X» 3 ( 8 «~ 3 (> \? 3? > 3 <( ( [ 3 z «> >( < ( 3 ( ( < ( 3 ( \ } 3 < (> 8 <?? ( 88? 3 3 [ \ ( 9 [ 93 >? 3 8 ( \? z ( 3 z ( X 8 3 <( ( ( [ [z ( [ «3 «X 8 3 ( «8 98 X»«3 X ( 9 (» > 38 > Q (3? ((( \ z 8 < { «(? ( ( X >» 8 «<? ( 939 (? ( \ 8 z

6 X 8 98 X? ( 8 z ( 8 «(? % } 9 8 } 3 X 3 3 ( [ [ 3 z z } ?? 3 X? X 3 ( ( z ([ ( ( ( 8 Q ( < ««( 3 > z \ > «3<8 «9» ( «3 [ 9 Z [ (? 8 «( «9 z (? 9««~ [ 89 «( } [ < ( z» ( «(» ( ( «# «( ( X (( } 3 } «8 > 3( >«z 9 >( ( Z%» [» ( >8 < 9 «}3? ( ( z ( ( (» ( { 9 9 > 8 8 (% [ ( ( (» >«( 8 3 «««Q «~ «# 9 9 ( XX X XXXX X ( ( ( ( ( 9» #» 3 8 Q ~ 9 ( Q Q 8 > >» Q Q ( > 3 3 «8 ( $ [ «( X 3 ( ( X X 9 #? ( ( ( $ (» z 3» 9 ( > ««[ 8 < < »» } Q«< > # 3 ( ( ( ( ««33 X>z 3 \» «<>» 9 3 «8? [ 8 «( < 9 <Q««9 < 9 Q $ «} ««\ 33 3 Q 39 ( 8 9 (8 9 8 ( Q Q Z 8 8 «~ «>(( «{ Q 8 { \ $»» ( 3 X 8 3( < ( X» < ( ~» «+«( ~ >» > X X 9 Z 3 X X 3 ( 3 98 < > < 3 Q 8 9 \ z «X 3 8 ( ( «( > 8 (? 3 [ 9 { \» 3«««~ ( ( (» ( # ( ( ( «< X (}» «9 » Q «< ( <3 >» 8» >

7 Q Q 98 ( 8?> 9 9 ( >»< < > #»» X Q> «\> <> 3 (? «> 38 3 < 8»> 33 Z = >«>?( 9»3 8 < ( «>» 3 8 ( X 39 Q8»? 8 < ( ««<«? 3 ( 3 3 ~ ( «9 9 <»? <»«<? [ < [ 9 z Q ( # «< % \ % 9 Q >» » (>< >< # > <( X 3 #» > 3 <«(> < «# X < «?» 3 X ««<X 3 «}8 ( 3 3 < 9 # ><? { > «[ ( > «< ««Q 9 Q «99 { 3 > Q «««\ 3 % 3 \ ( \ 9 [>»9» [ <? <? «9»? Q 3 z «> 8 «< > «<» Q 8 > > 3 ««<8 ~ Q #? Q?? «8 > 9<»» 83 8» 9 \ #? X =» 9 X9? «Q» Q { > «( }? 38 Q X \ > > 9 3? [ «<»=«3 X 8? 8 «> > < 8 < <»» 3 \«9 «< «8 3» \ 8?8 38 > ( \? ( » 3 «< >? 3 3» ( ( > > Q 3 ««3 ( \ 8 «< ~ 8 > ( < ?> 9 ( ( 3 < < z ( 3 «3 > 9 > ( 3 # 8<< 3 9» > <» 3»«( ( (Q 38 Z? 9 «9 9 ~ Q< ~» 3 > 98 «3» » > 3 z 8 } \ Q «9 3 < <>3 3 9 X? X > 3 98 >»» 3 \ 8 \ <> ( 3 ( Q 8» 9 ««> 8» > «> «{ <» 3 Q 3 < 3 8 > «8 >««( 3 3 > < (> 9 «8 < ««? Q 8 8 Q > «( < 9 3 < 3 8 8» 3 3» 9 [ 3 z > «X Q { 3 «# 8 3 ««9 3 } 8 3 X» «9? 9? 9 «> 8 <?8( Z 9 «( { > > 8 { »» \ ( > ( ~«3 8 [ > ( ( 3 «9 <» 9 «z «9 < «z 3 9 < <» («z % > 9 X X 99 3< «<<> > 9?»«Q ~ Q { ( 3 X» 8 8 Q 8 8 <»9 «< «<> ( 83 ( > «««\? 9 = < 3? 8 9 >? 8 «<8 3 9» 8 Q «Q «3 8 3 «> < [ > «3 ( 3 9 «3 >? 9 ~ < 9 «9?? > ( 3 8 > >> >8 9 (? 9 Q 8 [» < > 8? 9 (? «9 \««< 3 ««~ «8 QQ «< > <» 3 \»9 «( (?«> 3» ~? <<< > >»» <«>«< ( < z» «}» % ««X ~ > ~» > < > # ( 3 9 8\ } 8?< (» \««>«««3? z > >» 9 3 X > \?? + > Q Q 3 9 3»> < 8? z <«9 3»< #3> < 3 Z3 93»«} «? «>»»»«8< «««< > X >«[ » =» < < < >>» 9» 3 }««( } z}} ( [ > 3 «? < > 3 (? 3 \ >< 8 > >» «Q 9 X 3» 9 «9 [ [ > (? \ } >» (» ( 8 3 (< ( 3 «( <» < ( #»» X { < < ( 3 < < < 3 [ 9» \ > 3 3» «9 89 Q Q > «( ««<«3 ( «3 9 ( «3 «z 8 > 3 << 3 3 «9 «3 9 z 8 \» ( 3 ~ 3 3 3»<«3 «3««3 33 z 3 3 «8 Q <> X % X \ >»? «Q 9 3 ( z \ > 9 (» < <» \ «z > (» 3»» 3 «>>??? < [»( Q > 3» >< < 3 3»> <» «3» 3 «>» 3 «> ~»»» 9 8 3» 3? <3 9? < <««3 9 > ( z» 3 > { > [ « ( ( < 8» 3 3 > 3» (» 8 Q + 3 «3 3 8 > ««> } 3 «Q }# «< ( 8 z 3? Q 8 «( # Q 9 8 9?» «9 «9«««? #» > Q 3 «33 ~ > » #

Educjatipnal. L a d ie s * COBNWALILI.S H IG H SCHOOL. I F O R G IR L S A n B k i n d e r g a r t e n.

Educjatipnal. L a d ie s * COBNWALILI.S H IG H SCHOOL. I F O R G IR L S A n B k i n d e r g a r t e n. - - - 0 x ] - ) ) -? - Q - - z 0 x 8 - #? ) 80 0 0 Q ) - 8-8 - ) x ) - ) -] ) Q x?- x - - / - - x - - - x / /- Q ] 8 Q x / / - 0-0 0 x 8 ] ) / - - /- - / /? x ) x x Q ) 8 x q q q )- 8-0 0? - Q - - x?-

More information

' Liberty and Umou Ono and Inseparablo "

' Liberty and Umou Ono and Inseparablo 3 5? #< q 8 2 / / ) 9 ) 2 ) > < _ / ] > ) 2 ) ) 5 > x > [ < > < ) > _ ] ]? <

More information

MANY BILLS OF CONCERN TO PUBLIC

MANY BILLS OF CONCERN TO PUBLIC - 6 8 9-6 8 9 6 9 XXX 4 > -? - 8 9 x 4 z ) - -! x - x - - X - - - - - x 00 - - - - - x z - - - x x - x - - - - - ) x - - - - - - 0 > - 000-90 - - 4 0 x 00 - -? z 8 & x - - 8? > 9 - - - - 64 49 9 x - -

More information

PanHomc'r I'rui;* :".>r '.a'' W"»' I'fltolt. 'j'l :. r... Jnfii<on. Kslaiaaac. <.T i.. %.. 1 >

PanHomc'r I'rui;* :.>r '.a'' W»' I'fltolt. 'j'l :. r... Jnfii<on. Kslaiaaac. <.T i.. %.. 1 > 5 28 (x / &» )»(»»» Q ( 3 Q» (» ( (3 5» ( q 2 5 q 2 5 5 8) 5 2 2 ) ~ ( / x {» /»»»»» (»»» ( 3 ) / & Q ) X ] Q & X X X x» 8 ( &» 2 & % X ) 8 x & X ( #»»q 3 ( ) & X 3 / Q X»»» %» ( z 22 (»» 2» }» / & 2 X

More information

LOWELL WEEKI.Y JOURINAL

LOWELL WEEKI.Y JOURINAL / $ 8) 2 {!»!» X ( (!!!?! () ~ x 8» x /»!! $?» 8! ) ( ) 8 X x /! / x 9 ( 2 2! z»!!»! ) / x»! ( (»»!» [ ~!! 8 X / Q X x» ( (!»! Q ) X x X!! (? ( ()» 9 X»/ Q ( (X )!» / )! X» x / 6!»! }? ( q ( ) / X! 8 x»

More information

A. H. Hall, 33, 35 &37, Lendoi

A. H. Hall, 33, 35 &37, Lendoi 7 X x > - z Z - ----»»x - % x x» [> Q - ) < % - - 7»- -Q 9 Q # 5 - z -> Q x > z»- ~» - x " < z Q q»» > X»? Q ~ - - % % < - < - - 7 - x -X - -- 6 97 9

More information

LOWELL WEEKLY JOURNAL

LOWELL WEEKLY JOURNAL Y -» $ 5 Y 7 Y Y -Y- Q x Q» 75»»/ q } # ]»\ - - $ { Q» / X x»»- 3 q $ 9 ) Y q - 5 5 3 3 3 7 Q q - - Q _»»/Q Y - 9 - - - )- [ X 7» -» - )»? / /? Q Y»» # X Q» - -?» Q ) Q \ Q - - - 3? 7» -? #»»» 7 - / Q

More information

oenofc : COXT&IBCTOEU. AU skaacst sftwer thsa4 aafcekr will be ehat«s«ai Bi. C. W. JUBSSOS. PERFECT THBOUGH SDFFEBISG. our

oenofc : COXT&IBCTOEU. AU skaacst sftwer thsa4 aafcekr will be ehat«s«ai Bi. C. W. JUBSSOS. PERFECT THBOUGH SDFFEBISG. our x V - --- < x x 35 V? 3?/ -V 3 - ) - - [ Z8 - & Z - - - - - x 0-35 - 3 75 3 33 09 33 5 \ - - 300 0 ( -? 9 { - - - -- - < - V 3 < < - - Z 7 - z 3 - [ } & _ 3 < 3 ( 5 7< ( % --- /? - / 4-4 - & - % 4 V 2

More information

Neatest and Promptest Manner. E d i t u r ami rul)lihher. FOIt THE CIIILDIIES'. Trifles.

Neatest and Promptest Manner. E d i t u r ami rul)lihher. FOIt THE CIIILDIIES'. Trifles. » ~ $ ) 7 x X ) / ( 8 2 X 39 ««x» ««! «! / x? \» «({? «» q «(? (?? x! «? 8? ( z x x q? ) «q q q ) x z x 69 7( X X ( 3»«! ( ~«x ««x ) (» «8 4 X «4 «4 «8 X «x «(» X) ()»» «X «97 X X X 4 ( 86) x) ( ) z z

More information

Two Posts to Fill On School Board

Two Posts to Fill On School Board Y Y 9 86 4 4 qz 86 x : ( ) z 7 854 Y x 4 z z x x 4 87 88 Y 5 x q x 8 Y 8 x x : 6 ; : 5 x ; 4 ( z ; ( ) ) x ; z 94 ; x 3 3 3 5 94 ; ; ; ; 3 x : 5 89 q ; ; x ; x ; ; x : ; ; ; ; ; ; 87 47% : () : / : 83

More information

A DARK GREY P O N T, with a Switch Tail, and a small Star on the Forehead. Any

A DARK GREY P O N T, with a Switch Tail, and a small Star on the Forehead. Any Y Y Y X X «/ YY Y Y ««Y x ) & \ & & } # Y \#$& / Y Y X» \\ / X X X x & Y Y X «q «z \x» = q Y # % \ & [ & Z \ & { + % ) / / «q zy» / & / / / & x x X / % % ) Y x X Y $ Z % Y Y x x } / % «] «] # z» & Y X»

More information

Governor Green Triumphs Over Mudslinging

Governor Green Triumphs Over Mudslinging ; XXX 6 928 - x 22 5 Q 0 x 2- Q- & & x 30 - x 93000000 95000000 50 000 x 0:30 7 7 2 x q 9 0 0:30 2;00 7:30 9 ( 9 & ( ( - ( - 225000 x ( ( 800 ) - 70000 200000 - x ; 200-0: 3333 0850; 778: 5-38 090; 002;

More information

a s*:?:; -A: le London Dyers ^CleanefSt * S^d. per Y ard. -P W ..n 1 0, , c t o b e e d n e sd *B A J IllW6fAi>,EB. E D U ^ T IG r?

a s*:?:; -A: le London Dyers ^CleanefSt * S^d. per Y ard. -P W ..n 1 0, , c t o b e e d n e sd *B A J IllW6fAi>,EB. E D U ^ T IG r? ? 9 > 25? < ( x x 52 ) < x ( ) ( { 2 2 8 { 28 ] ( 297 «2 ) «2 2 97 () > Q ««5 > «? 2797 x 7 82 2797 Q z Q (

More information

LOWELL WEEKLY JOURNAL. ^Jberxy and (Jmott Oao M d Ccmsparftble. %m >ai ruv GEEAT INDUSTRIES

LOWELL WEEKLY JOURNAL. ^Jberxy and (Jmott Oao M d Ccmsparftble. %m >ai ruv GEEAT INDUSTRIES ? (») /»» 9 F ( ) / ) /»F»»»»»# F??»»» Q ( ( »»» < 3»» /» > > } > Q ( Q > Z F 5

More information

r/lt.i Ml s." ifcr ' W ATI II. The fnncrnl.icniccs of Mr*. John We mil uppn our tcpiiblicnn rcprc Died.

r/lt.i Ml s. ifcr ' W ATI II. The fnncrnl.icniccs of Mr*. John We mil uppn our tcpiiblicnn rcprc Died. $ / / - (\ \ - ) # -/ ( - ( [ & - - - - \ - - ( - - - - & - ( ( / - ( \) Q & - - { Q ( - & - ( & q \ ( - ) Q - - # & - - - & - - - $ - 6 - & # - - - & -- - - - & 9 & q - / \ / - - - -)- - ( - - 9 - - -

More information

LOWHLL #WEEKLY JOURNAL.

LOWHLL #WEEKLY JOURNAL. # F 7 F --) 2 9 Q - Q - - F - x $ 2 F? F \ F q - x q - - - - )< - -? - F - - Q z 2 Q - x -- - - - 3 - % 3 3 - - ) F x - \ - - - - - q - q - - - - -z- < F 7-7- - Q F 2 F - F \x -? - - - - - z - x z F -

More information

.1 "patedl-righl" timti tame.nto our oai.c iii C. W.Fiak&Co. She ftowtt outnal,

.1 patedl-righl timti tame.nto our oai.c iii C. W.Fiak&Co. She ftowtt outnal, J 2 X Y J Y 3 : > Y 6? ) Q Y x J Y Y // 6 : : \ x J 2 J Q J Z 3 Y 7 2 > 3 [6 2 : x z (7 :J 7 > J : 7 (J 2 J < ( q / 3 6 q J $3 2 6:J : 3 q 2 6 3 2 2 J > 2 :2 : J J 2 2 J 7 J 7 J \ : q 2 J J Y q x ( ) 3:

More information

LOWELL WEEKLY JOURNAL

LOWELL WEEKLY JOURNAL G $ G 2 G ««2 ««q ) q «\ { q «««/ 6 «««««q «] «q 6 ««Z q «««Q \ Q «q «X ««G X G ««? G Q / Q Q X ««/«X X «««Q X\ «q «X \ / X G XX «««X «x «X «x X G X 29 2 ««Q G G «) 22 G XXX GG G G G G G X «x G Q «) «G

More information

LOWELL JOURNAL. MUST APOLOGIZE. such communication with the shore as Is m i Boimhle, noewwary and proper for the comfort

LOWELL JOURNAL. MUST APOLOGIZE. such communication with the shore as Is m i Boimhle, noewwary and proper for the comfort - 7 7 Z 8 q ) V x - X > q - < Y Y X V - z - - - - V - V - q \ - q q < -- V - - - x - - V q > x - x q - x q - x - - - 7 -» - - - - 6 q x - > - - x - - - x- - - q q - V - x - - ( Y q Y7 - >»> - x Y - ] [

More information

A L T O SOLO LOWCLL. MICHIGAN, THURSDAY. DECEMBER 10,1931. ritt. Mich., to T h e Heights. Bos" l u T H I S COMMl'NiTY IN Wilcox

A L T O SOLO LOWCLL. MICHIGAN, THURSDAY. DECEMBER 10,1931. ritt. Mich., to T h e Heights. Bos l u T H I S COMMl'NiTY IN Wilcox G 093 < 87 G 9 G 4 4 / - G G 3 -!! - # -G G G : 49 q» - 43 8 40 - q - z 4 >» «9 0-9 - - q 00! - - q q!! ) 5 / : \ 0 5 - Z : 9 [ -?! : ) 5 - - > - 8 70 / q - - - X!! - [ 48 - -!

More information

Q SON,' (ESTABLISHED 1879L

Q SON,' (ESTABLISHED 1879L ( < 5(? Q 5 9 7 00 9 0 < 6 z 97 ( # ) $ x 6 < ( ) ( ( 6( ( ) ( $ z 0 z z 0 ) { ( % 69% ( ) x 7 97 z ) 7 ) ( ) 6 0 0 97 )( 0 x 7 97 5 6 ( ) 0 6 ) 5 ) 0 ) 9%5 z» 0 97 «6 6» 96? 0 96 5 0 ( ) ( ) 0 x 6 0

More information

LOWELL WEEKLY JOURNAL.

LOWELL WEEKLY JOURNAL. Y $ Y Y 7 27 Y 2» x 7»» 2» q» ~ [ } q q $ $ 6 2 2 2 2 2 2 7 q > Y» Y >» / Y» ) Y» < Y»» _»» < Y > Y Y < )»» >» > ) >» >> >Y x x )»» > Y Y >>»» }> ) Y < >» /» Y x» > / x /»»»»» >» >» >»» > > >» < Y /~ >

More information

Pithy P o i n t s Picked I ' p and Patljr Put By Our P e r i p a tetic Pencil Pusher VOLUME X X X X. Lee Hi^h School Here Friday Ni^ht

Pithy P o i n t s Picked I ' p and Patljr Put By Our P e r i p a tetic Pencil Pusher VOLUME X X X X. Lee Hi^h School Here Friday Ni^ht G G QQ K K Z z U K z q Z 22 x z - z 97 Z x z j K K 33 G - 72 92 33 3% 98 K 924 4 G G K 2 G x G K 2 z K j x x 2 G Z 22 j K K x q j - K 72 G 43-2 2 G G z G - -G G U q - z q - G x) z q 3 26 7 x Zz - G U-

More information

AanumntBAasciAs. l e t e s auas trasuarbe, amtima*. pay Bna. aaeh t!iacttign. Xat as eling te Trndi'aBd^glit!

AanumntBAasciAs. l e t e s auas trasuarbe, amtima*. pay Bna. aaeh t!iacttign. Xat as eling te Trndi'aBd^glit! - [ - --- --- ~ - 5 4 G 4? G 8 0 0 0 7 0 - Q - - - 6 8 7 2 75 00 - [ 7-6 - - Q - ] z - 9 - G - 0 - - z / - ] G / - - 4-6 7 - z - 6 - - z - - - - - - G z / - - - G 0 Zz 4 z4 5? - - Z z 2 - - {- 9 9? Z G

More information

E S T A B L IS H E D. n AT Tnn G.D.O. r.w.-bal'eu. e d n e s d a y. II GRANVILLE HOUSE. GATJDICK ROAD. MEADS. EASTBOUENk

E S T A B L IS H E D. n AT Tnn G.D.O. r.w.-bal'eu. e d n e s d a y. II GRANVILLE HOUSE. GATJDICK ROAD. MEADS. EASTBOUENk K q X k K 5 ) ) 5 / K K x x) )? //? q? k X z K 8 5 5? K K K / / $8 ± K K K 8 K / 8 K K X k k X ) k k /» / K / / / k / ] 5 % k / / k k? Z k K ] 8 K K K )» 5 ) # 8 q»)kk q»» )88{ k k k k / k K X 8 8 8 ]

More information

d A L. T O S O U LOWELL, MICHIGAN. THURSDAY, DECEMBER 5, 1929 Cadillac, Nov. 20. Indignation

d A L. T O S O U LOWELL, MICHIGAN. THURSDAY, DECEMBER 5, 1929 Cadillac, Nov. 20. Indignation ) - 5 929 XXX - $ 83 25 5 25 $ ( 2 2 z 52 $9285)9 7 - - 2 72 - - 2 3 zz - 9 86 - - - - 88 - q 2 882 q 88 - - - - - - ( 89 < - Q - 857-888 - - - & - - q - { q 7 - - - - q - - - - - - q - - - - 929 93 q

More information

LOWELL WEEKLY JOURNAL.

LOWELL WEEKLY JOURNAL. Y 5 ; ) : Y 3 7 22 2 F $ 7 2 F Q 3 q q 6 2 3 6 2 5 25 2 2 3 $2 25: 75 5 $6 Y q 7 Y Y # \ x Y : { Y Y Y : ( \ _ Y ( ( Y F [ F F ; x Y : ( : G ( ; ( ~ x F G Y ; \ Q ) ( F \ Q / F F \ Y () ( \ G Y ( ) \F

More information

i r-s THE MEMPHIS, TENN., SATURDAY. DEGfMBER

i r-s THE MEMPHIS, TENN., SATURDAY. DEGfMBER N k Q2 90 k ( < 5 q v k 3X3 0 2 3 Q :: Y? X k 3 : \ N 2 6 3 N > v N z( > > :}9 [ ( k v >63 < vq 9 > k k x k k v 6> v k XN Y k >> k < v Y X X X NN Y 2083 00 N > N Y Y N 0 \ 9>95 z {Q ]k3 Q k x k k z x X

More information

V o l u m e 5, N u m b e r 5 2, 1 6 P a g e s. Gold B e U ClUt Stamps Double Stamp D a y E v e r y Wednesday

V o l u m e 5, N u m b e r 5 2, 1 6 P a g e s. Gold B e U ClUt Stamps Double Stamp D a y E v e r y Wednesday 1 6 5 J 9 6 " " z k ; k x k k k z z k j " " ( k " " k 8 1959 " " x k j 5 25 ; ; k k qz ; x 13 x k * k ( ) k k : qz 13 k k k j ; q k x ; x 615 26 ( : k z 113 99751 z k k q ; 15 k k k j q " " k j x x ( *»

More information

County Council Named for Kent

County Council Named for Kent \ Y Y 8 9 69 6» > 69 ««] 6 : 8 «V z 9 8 x 9 8 8 8?? 9 V q» :: q;; 8 x () «; 8 x ( z x 9 7 ; x >«\ 8 8 ; 7 z x [ q z «z : > ; ; ; ( 76 x ; x z «7 8 z ; 89 9 z > q _ x 9 : ; 6? ; ( 9 [ ) 89 _ ;»» «; x V

More information

OWELL WEEKLY JOURNAL

OWELL WEEKLY JOURNAL Y \»< - } Y Y Y & #»»» q ] q»»»>) & - - - } ) x ( - { Y» & ( x - (» & )< - Y X - & Q Q» 3 - x Q Y 6 \Y > Y Y X 3 3-9 33 x - - / - -»- --

More information

LOWELL WEEKLY JOURNAL

LOWELL WEEKLY JOURNAL Y G q G Y Y 29 8 $ 29 G 6 q )

More information

A Memorial. Death Crash Branch Out. Symbol The. at Crossing Flaming Poppy. in Belding

A Memorial. Death Crash Branch Out. Symbol The. at Crossing Flaming Poppy. in Belding - G Y Y 8 9 XXX G - Y - Q 5 8 G Y G Y - - * Y G G G G 9 - G - - : - G - - ) G G- Y G G q G G : Q G Y G 5) Y : z 6 86 ) ; - ) z; G ) 875 ; ) ; G -- ) ; Y; ) G 8 879 99 G 9 65 q 99 7 G : - G G Y ; - G 8

More information

LOWELL WEEKLY JOURNAL

LOWELL WEEKLY JOURNAL W WY R G «( 5 R 5 Y q YG R ««W G WY Y 7 W \(\ 5 R ( W R R W ) W «W W W W< W ) W 53 R R Y 4 RR \ \ ( q ) W W X R R RY \ 73 «\ 2 «W R RG ( «q ) )[ 5 7 G ««R q ] 6 ) X 5 5 x / ( 2 3 4 W «(«\Y W Q RY G G )

More information

and A L T O S O L O LOWELL, MICHIGAN, THURSDAY, OCTCBER Mrs. Thomas' Young Men Good Bye 66 Long Illness Have Sport in

and A L T O S O L O LOWELL, MICHIGAN, THURSDAY, OCTCBER Mrs. Thomas' Young Men Good Bye 66 Long Illness Have Sport in 5 7 8 x z!! Y! [! 2 &>3 x «882 z 89 q!!! 2 Y 66 Y $ Y 99 6 x x 93 x 7 8 9 x 5$ 4 Y q Q 22 5 3 Z 2 5 > 2 52 2 $ 8» Z >!? «z???? q > + 66 + + ) ( x 4 ~ Y Y»» x ( «/ ] x ! «z x( ) x Y 8! < 6 x x 8 \ 4\

More information

SPIRITUALISM. forces. of Spirit, A n stiy a e d f r o m a C o m m o n rhey. n o d and H en so S ta n d p o in t. Lea d s i 1 T U A L I.S M.

SPIRITUALISM. forces. of Spirit, A n stiy a e d f r o m a C o m m o n rhey. n o d and H en so S ta n d p o in t. Lea d s i 1 T U A L I.S M. ~ 3 : K G V 7 G GG 2 3 9 3» < V ; j z_! V 9 7 ' ; > : ; _ < - «-] 88 _ K _ [ -] ZZ - - _ [ ) G K < ' - - ( - '! j () - -] < : : < :?! q z ; [ > # : - 2 - - j ; :!_ - ] ' z ; : j G - j j - [ _ j! { q -

More information

1 h 9 e $ s i n t h e o r y, a p p l i c a t i a n

1 h 9 e $ s i n t h e o r y, a p p l i c a t i a n T : 99 9 \ E \ : \ 4 7 8 \ \ \ \ - \ \ T \ \ \ : \ 99 9 T : 99-9 9 E : 4 7 8 / T V 9 \ E \ \ : 4 \ 7 8 / T \ V \ 9 T - w - - V w w - T w w \ T \ \ \ w \ w \ - \ w \ \ w \ \ \ T \ w \ w \ w \ w \ \ w \

More information

MEMORIAL UNIVERSITY OF NEWFOUNDLAND

MEMORIAL UNIVERSITY OF NEWFOUNDLAND MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS Section 5. Math 090 Fall 009 SOLUTIONS. a) Using long division of polynomials, we have x + x x x + ) x 4 4x + x + 0x x 4 6x

More information

Lesson 24: Using the Quadratic Formula,

Lesson 24: Using the Quadratic Formula, , b ± b 4ac x = a Opening Exercise 1. Examine the two equation below and discuss what is the most efficient way to solve each one. A. 4xx + 5xx + 3 = xx 3xx B. cc 14 = 5cc. Solve each equation with the

More information

LOWELL WEEKLY JOURNAL.

LOWELL WEEKLY JOURNAL. > LLL KLY L L x L L L L G K Y F 7 2 K LKL Y K «F «««««q 5 $ ) / «2 K) ««) 74 «G > x «LY K «! «KL K K K K K! ««x > x K! K ) 2 K «X! «K LK >> < >«««) «< >>«K«KLK < «4! «««#> ««!

More information

F.3 Special Factoring and a General Strategy of Factoring

F.3 Special Factoring and a General Strategy of Factoring F.3 Special Factoring and a General Strategy of Factoring Difference of Squares section F4 233 Recall that in Section P2, we considered formulas that provide a shortcut for finding special products, such

More information

Lowell Dam Gone Out. Streets Turned I n t o Rivers. No Cause For Alarm Now However As This Happened 35 Years A&o

Lowell Dam Gone Out. Streets Turned I n t o Rivers. No Cause For Alarm Now However As This Happened 35 Years A&o V ()\\ ))? K K Y 6 96 Y - Y Y V 5 Z ( z x z \ - \ - - z - q q x x - x 5 9 Q \ V - - Y x 59 7 x x - Y - x - - x z - z x - ( 7 x V 9 z q &? - 9 - V ( x - - - V- [ Z x z - -x > -) - - > X Z z ( V V V

More information

M E M P H I S, T E N N., S A T U E D A Y, OCTOBER 8, 1870.

M E M P H I S, T E N N., S A T U E D A Y, OCTOBER 8, 1870. 5 L V 8 5 x - L : L Q ) L - \ \ Q Q - V 84 z < L L 4 Y z ( (

More information

LOWELL WEEKLY JOURNAL

LOWELL WEEKLY JOURNAL : Y J G V $ 5 V V G Y 2 25 Y 2» 5 X # VG q q q 6 6 X J 6 $3 ( 6 2 6 2 6 25 3 2 6 Y q 2 25: JJ JJ < X Q V J J Y J Q V (» Y V X Y? G # V Y J J J G J»Y ) J J / J Y Y X ({ G #? J Y ~» 9? ) < ( J VY Y J G (

More information

Confidence Intervals for the Interaction Odds Ratio in Logistic Regression with Two Binary X s

Confidence Intervals for the Interaction Odds Ratio in Logistic Regression with Two Binary X s Chapter 867 Confidence Intervals for the Interaction Odds Ratio in Logistic Regression with Two Binary X s Introduction Logistic regression expresses the relationship between a binary response variable

More information

LOWELL. MICHIGAN. WEDNESDAY, FEBRUARY NUMllEE 33, Chicago. >::»«ad 0:30am, " 16.n«l w 00 ptn Jaekten,.'''4snd4:4(>a tii, ijilwopa

LOWELL. MICHIGAN. WEDNESDAY, FEBRUARY NUMllEE 33, Chicago. >::»«ad 0:30am,  16.n«l w 00 ptn Jaekten,.'''4snd4:4(>a tii, ijilwopa 4/X6 X 896 & # 98 # 4 $2 q $ 8 8 $ 8 6 8 2 8 8 2 2 4 2 4 X q q!< Q 48 8 8 X 4 # 8 & q 4 ) / X & & & Q!! & & )! 2 ) & / / ;) Q & & 8 )

More information

JUST THE MATHS UNIT NUMBER ORDINARY DIFFERENTIAL EQUATIONS 3 (First order equations (C)) A.J.Hobson

JUST THE MATHS UNIT NUMBER ORDINARY DIFFERENTIAL EQUATIONS 3 (First order equations (C)) A.J.Hobson JUST THE MATHS UNIT NUMBER 15.3 ORDINARY DIFFERENTIAL EQUATIONS 3 (First order equations (C)) by A.J.Hobson 15.3.1 Linear equations 15.3.2 Bernouilli s equation 15.3.3 Exercises 15.3.4 Answers to exercises

More information

Discrete Structures Lecture 5

Discrete Structures Lecture 5 Introduction EXAMPLE 1 Express xx yy(xx + yy = 0) without the existential quantifier. Solution: xx yy(xx + yy = 0) is the same as xxxx(xx) where QQ(xx) is yyyy(xx, yy) and PP(xx, yy) = xx + yy = 0 EXAMPLE

More information

Sect Least Common Denominator

Sect Least Common Denominator 4 Sect.3 - Least Common Denominator Concept #1 Writing Equivalent Rational Expressions Two fractions are equivalent if they are equal. In other words, they are equivalent if they both reduce to the same

More information

Lesson 23: Deriving the Quadratic Formula

Lesson 23: Deriving the Quadratic Formula : Deriving the Quadratic Formula Opening Exercise 1. Solve for xx. xx 2 + 2xx = 8 7xx 2 12xx + 4 = 0 Discussion 2. Which of these problems makes more sense to solve by completing the square? Which makes

More information

Wayfarer Traveler. The. Laura. Most of us enjoy. Family and multi-generational travel. The Luxury of Togetherness. Happy Traveling, Owner s

Wayfarer Traveler. The. Laura. Most of us enjoy. Family and multi-generational travel. The Luxury of Togetherness. Happy Traveling, Owner s 6, z j Kw x w 8- x - w w w; x w w z, K, x -, w w w, w! x w j w w x z w w J w w w, w w w x w w w w 6, w q, w x, w x x, w Q, w 3-, w,, -w 6 ;, w x w w-- w j -, -, x, - -,, -,, w,, w w w, w w w, - w, w,,

More information

' '-'in.-i 1 'iritt in \ rrivfi pr' 1 p. ru

' '-'in.-i 1 'iritt in \ rrivfi pr' 1 p. ru V X X Y Y 7 VY Y Y F # < F V 6 7»< V q q $ $» q & V 7» Q F Y Q 6 Q Y F & Q &» & V V» Y V Y [ & Y V» & VV & F > V } & F Q \ Q \» Y / 7 F F V 7 7 x» > QX < #» > X >» < F & V F» > > # < q V 6 & Y Y q < &

More information

Jim Lambers MAT 280 Summer Semester Practice Final Exam Solution. dy + xz dz = x(t)y(t) dt. t 3 (4t 3 ) + e t2 (2t) + t 7 (3t 2 ) dt

Jim Lambers MAT 280 Summer Semester Practice Final Exam Solution. dy + xz dz = x(t)y(t) dt. t 3 (4t 3 ) + e t2 (2t) + t 7 (3t 2 ) dt Jim Lambers MAT 28 ummer emester 212-1 Practice Final Exam olution 1. Evaluate the line integral xy dx + e y dy + xz dz, where is given by r(t) t 4, t 2, t, t 1. olution From r (t) 4t, 2t, t 2, we obtain

More information

s f o r s o l v i n g t h e n o n l i n

s f o r s o l v i n g t h e n o n l i n M M R M q q D O : q 7 8 q q q M q x- q M M M 9 R R D O : 78 / x q D MO : M 7 9 8 / D q P F x z M q M q D T P - z P G S F q q q q q q q D q q PZ w - z q - P q q q w q q q w q q w z q - w P w q w w - w w

More information

Lecture 3. Logic Predicates and Quantified Statements Statements with Multiple Quantifiers. Introduction to Proofs. Reading (Epp s textbook)

Lecture 3. Logic Predicates and Quantified Statements Statements with Multiple Quantifiers. Introduction to Proofs. Reading (Epp s textbook) Lecture 3 Logic Predicates and Quantified Statements Statements with Multiple Quantifiers Reading (Epp s textbook) 3.1-3.3 Introduction to Proofs Reading (Epp s textbook) 4.1-4.2 1 Propositional Functions

More information

Crew of25 Men Start Monday On Showboat. Many Permanent Improvements To Be Made;Project Under WPA

Crew of25 Men Start Monday On Showboat. Many Permanent Improvements To Be Made;Project Under WPA U G G G U 2 93 YX Y q 25 3 < : z? 0 (? 8 0 G 936 x z x z? \ 9 7500 00? 5 q 938 27? 60 & 69? 937 q? G x? 937 69 58 } x? 88 G # x 8 > x G 0 G 0 x 8 x 0 U 93 6 ( 2 x : X 7 8 G G G q x U> x 0 > x < x G U 5

More information

Jim Lambers MAT 280 Fall Semester Practice Final Exam Solution

Jim Lambers MAT 280 Fall Semester Practice Final Exam Solution Jim Lambers MAT 8 Fall emester 6-7 Practice Final Exam olution. Use Lagrange multipliers to find the point on the circle x + 4 closest to the point (, 5). olution We have f(x, ) (x ) + ( 5), the square

More information

REAL WORLD SCENARIOS: PART IV {mostly for those wanting 114 or higher} 1. If 4x + y = 110 where 10 < x < 20, what is the least possible value of y?

REAL WORLD SCENARIOS: PART IV {mostly for those wanting 114 or higher} 1. If 4x + y = 110 where 10 < x < 20, what is the least possible value of y? REAL WORLD SCENARIOS: PART IV {mostly for those wanting 114 or higher} REAL WORLD SCENARIOS 1. If 4x + y = 110 where 10 < x < 0, what is the least possible value of y? WORK AND ANSWER SECTION. Evaluate

More information

Discrete Mathematics Recitation Course 張玟翔

Discrete Mathematics Recitation Course 張玟翔 Discrete Mathematics Recitation Course 1 2013.03.07 張玟翔 Acknowledge 鄭安哲 TA 2012 About Myself English Name : Zak Chinese Name : 張玟翔 Mail:o0000032@yahoo.com.tw Lab: ED612 1-1 Propositional Logic 1-1 Ex.2

More information

Nuclear Quadrupole Resonance Spectroscopy. Some examples of nuclear quadrupole moments

Nuclear Quadrupole Resonance Spectroscopy. Some examples of nuclear quadrupole moments Nuclear Quadrupole Resonance Spectroscopy Review nuclear quadrupole moments, Q A negative value for Q denotes a distribution of charge that is "football-shaped", i.e. a sphere elongated at the poles; a

More information

Discrete Structures Lecture Predicates and Quantifiers

Discrete Structures Lecture Predicates and Quantifiers Introduction In this section we will introduce a more powerful type of logic called predicate logic. Predicates Consider the statement: xx > 3. The statement has two parts: 1. the variable, xx and 2. the

More information

Lesson 8: Absolute Value Equations

Lesson 8: Absolute Value Equations Warm-Up Exercise 1. Watch the absolute value video on YouTube Math Shorts Episode 10 and then answer the questions below. https://www.youtube.com/watch?v=wrof6dw63es A. 1.3 = B. 4.75 = C. 10 + 4 = D. 11

More information

Additional Practice Lessons 2.02 and 2.03

Additional Practice Lessons 2.02 and 2.03 Additional Practice Lessons 2.02 and 2.03 1. There are two numbers n that satisfy the following equations. Find both numbers. a. n(n 1) 306 b. n(n 1) 462 c. (n 1)(n) 182 2. The following function is defined

More information

10.1 Three Dimensional Space

10.1 Three Dimensional Space Math 172 Chapter 10A notes Page 1 of 12 10.1 Three Dimensional Space 2D space 0 xx.. xx-, 0 yy yy-, PP(xx, yy) [Fig. 1] Point PP represented by (xx, yy), an ordered pair of real nos. Set of all ordered

More information

Course 2BA1: Hilary Term 2007 Section 8: Quaternions and Rotations

Course 2BA1: Hilary Term 2007 Section 8: Quaternions and Rotations Course BA1: Hilary Term 007 Section 8: Quaternions and Rotations David R. Wilkins Copyright c David R. Wilkins 005 Contents 8 Quaternions and Rotations 1 8.1 Quaternions............................ 1 8.

More information

On the polynomial x(x + 1)(x + 2)(x + 3)

On the polynomial x(x + 1)(x + 2)(x + 3) On the polynomial x(x + 1)(x + 2)(x + 3) Warren Sinnott, Steven J Miller, Cosmin Roman February 27th, 2004 Abstract We show that x(x + 1)(x + 2)(x + 3) is never a perfect square or cube for x a positive

More information

2.1 NUMERICAL SOLUTION OF SIMULTANEOUS FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS. differential equations with the initial values y(x 0. ; l.

2.1 NUMERICAL SOLUTION OF SIMULTANEOUS FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS. differential equations with the initial values y(x 0. ; l. Numerical Methods II UNIT.1 NUMERICAL SOLUTION OF SIMULTANEOUS FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS.1.1 Runge-Kutta Method of Fourth Order 1. Let = f x,y,z, = gx,y,z be the simultaneous first order

More information

LOWELL, MICHIGAN, NOVEMBER 27, Enroute to Dominican Republic

LOWELL, MICHIGAN, NOVEMBER 27, Enroute to Dominican Republic LDG L G L Y Y LLL G 7 94 D z G L D! G G! L $ q D L! x 9 94 G L L L L L q G! 94 D 94 L L z # D = 4 L ( 4 Q ( > G D > L 94 9 D G z ] z ) q 49 4 L [ ( D x ] LY z! q x x < G 7 ( L! x! / / > ( [ x L G q x!

More information

HEAGAN & CO., OPP. f>, L. & W. DEPOT, DOYER, N. J, OUR MOTTO! ould Iwv ia immediate vltlui. VEEY BEST NEW Creamery Butter 22c ib,

HEAGAN & CO., OPP. f>, L. & W. DEPOT, DOYER, N. J, OUR MOTTO! ould Iwv ia immediate vltlui. VEEY BEST NEW Creamery Butter 22c ib, #4 NN N G N N % XX NY N Y FY N 2 88 N 28 k N k F P X Y N Y /» 2«X ««!!! 8 P 3 N 0»9! N k 25 F $ 60 $3 00 $3000 k k N 30 Y F00 6 )P 0» «{ N % X zz» «3 0««5 «N «XN» N N 00/ N 4 GN N Y 07 50 220 35 2 25 0

More information

Lesson 14: Solving Inequalities

Lesson 14: Solving Inequalities Hart Interactive Algebra 1 Lesson 14 Classwork 1. Consider the inequality xx 2 + 4xx 5. a. Think about some possible values to assign to xx that make this inequality a true statement. Find at least two

More information

Complex Variables. Chapter 1. Complex Numbers Section 1.2. Basic Algebraic Properties Proofs of Theorems. December 16, 2016

Complex Variables. Chapter 1. Complex Numbers Section 1.2. Basic Algebraic Properties Proofs of Theorems. December 16, 2016 Complex Variables Chapter 1. Complex Numbers Section 1.2. Basic Algebraic Properties Proofs of Theorems December 16, 2016 () Complex Variables December 16, 2016 1 / 12 Table of contents 1 Theorem 1.2.1

More information

ACCEPTS HUGE FLORAL KEY TO LOWELL. Mrs, Walter Laid to Rest Yesterday

ACCEPTS HUGE FLORAL KEY TO LOWELL. Mrs, Walter Laid to Rest Yesterday $ j < < < > XXX Y 928 23 Y Y 4% Y 6 -- Q 5 9 2 5 Z 48 25 )»-- [ Y Y Y & 4 j q - Y & Y 7 - -- - j \ -2 -- j j -2 - - - - [ - - / - ) ) - - / j Y 72 - ) 85 88 - / X - j ) \ 7 9 Y Y 2 3» - ««> Y 2 5 35 Y

More information

Kent Co. Received Red Cross Service Abundantly in ' 4 9 E

Kent Co. Received Red Cross Service Abundantly in ' 4 9 E G N GN Y 95 89 N - q» B < ) < - 9 - - - - q ( B 6 - q - Q» x x 8 {) N - 9» -

More information

Homework 1/Solutions. Graded Exercises

Homework 1/Solutions. Graded Exercises MTH 310-3 Abstract Algebra I and Number Theory S18 Homework 1/Solutions Graded Exercises Exercise 1. Below are parts of the addition table and parts of the multiplication table of a ring. Complete both

More information

Polynomials. In many problems, it is useful to write polynomials as products. For example, when solving equations: Example:

Polynomials. In many problems, it is useful to write polynomials as products. For example, when solving equations: Example: Polynomials Monomials: 10, 5x, 3x 2, x 3, 4x 2 y 6, or 5xyz 2. A monomial is a product of quantities some of which are unknown. Polynomials: 10 + 5x 3x 2 + x 3, or 4x 2 y 6 + 5xyz 2. A polynomial is a

More information

Ayuntamiento de Madrid

Ayuntamiento de Madrid 9 v vx-xvv \ ü - v q v ó - ) q ó v Ó ü " v" > - v x -- ü ) Ü v " ñ v é - - v j? j 7 Á v ü - - v - ü

More information

F.1 Greatest Common Factor and Factoring by Grouping

F.1 Greatest Common Factor and Factoring by Grouping 1 Factoring Factoring is the reverse process of multiplication. Factoring polynomials in algebra has similar role as factoring numbers in arithmetic. Any number can be expressed as a product of prime numbers.

More information

Lesson 25: Using the Quadratic Formula,

Lesson 25: Using the Quadratic Formula, , b ± b 4ac x = a Opening Exercise Over the years, many students and teachers have thought of ways to help us all remember the quadratic formula. Below is the YouTube link to a video created by two teachers

More information

2. Similarly, 8 following generalization: The denominator of the rational exponent is the index of the radical.

2. Similarly, 8 following generalization: The denominator of the rational exponent is the index of the radical. RD. Rational Exponents Rational Exponents In sections P and RT, we reviewed properties of powers with natural and integral exponents. All of these properties hold for real exponents as well. In this section,

More information

Closed-Form Solution Of Absolute Orientation Using Unit Quaternions

Closed-Form Solution Of Absolute Orientation Using Unit Quaternions Closed-Form Solution Of Absolute Orientation Using Unit Berthold K. P. Horn Department of Computer and Information Sciences November 11, 2004 Outline 1 Introduction 2 3 The Problem Given: two sets of corresponding

More information

Worksheets for GCSE Mathematics. Quadratics. mr-mathematics.com Maths Resources for Teachers. Algebra

Worksheets for GCSE Mathematics. Quadratics. mr-mathematics.com Maths Resources for Teachers. Algebra Worksheets for GCSE Mathematics Quadratics mr-mathematics.com Maths Resources for Teachers Algebra Quadratics Worksheets Contents Differentiated Independent Learning Worksheets Solving x + bx + c by factorisation

More information

Chapter 2: Heat Conduction Equation

Chapter 2: Heat Conduction Equation -1 General Relation for Fourier s Law of Heat Conduction - Heat Conduction Equation -3 Boundary Conditions and Initial Conditions -1 General Relation for Fourier s Law of Heat Conduction (1) The rate of

More information

We say that a polynomial is in the standard form if it is written in the order of decreasing exponents of x. Operations on polynomials:

We say that a polynomial is in the standard form if it is written in the order of decreasing exponents of x. Operations on polynomials: R.4 Polynomials in one variable A monomial: an algebraic expression of the form ax n, where a is a real number, x is a variable and n is a nonnegative integer. : x,, 7 A binomial is the sum (or difference)

More information

Name (Print) ME Mechanics of Materials Exam # 2 Date: March 29, 2016 Time: 8:00 10:00 PM - Location: PHYS 114

Name (Print) ME Mechanics of Materials Exam # 2 Date: March 29, 2016 Time: 8:00 10:00 PM - Location: PHYS 114 Name (Print) (Last) (First) Instructions: ME 323 - Mechanics of Materials Exam # 2 Date: March 29, 2016 Time: 8:00 10:00 PM - Location: PHYS 114 Circle your lecturer s name and your class meeting time.

More information

Lesson 7: Watch Your Step!

Lesson 7: Watch Your Step! In previous lessons, we have looked at techniques for solving equations, a common theme throughout algebra. In this lesson, we examine some potential dangers where our intuition about algebra may need

More information

Simplifying Rational Expressions and Functions

Simplifying Rational Expressions and Functions Department of Mathematics Grossmont College October 15, 2012 Recall: The Number Types Definition The set of whole numbers, ={0, 1, 2, 3, 4,...} is the set of natural numbers unioned with zero, written

More information

LOWELL WEEKLY JOURNAL

LOWELL WEEKLY JOURNAL KY Y 872 K & q $ < 9 2 q 4 8 «7 K K K «> 2 26 8 5 4 4 7»» 2 & K q 4 [«5 «$6 q X «K «8K K88 K 7 ««$25 K Q ««q 8 K K Y & 7K /> Y 8«#»«Y 87 8 Y 4 KY «7««X & Y» K ) K K 5 KK K > K» Y Y 8 «KK > /» >» 8 K X

More information

and Union One end Inseparable." LOWELL. MICHIGAN. WEDNESDAY. JUNE HUMPHBHT'S HOMEOPATHIC SPECIFICS

and Union One end Inseparable. LOWELL. MICHIGAN. WEDNESDAY. JUNE HUMPHBHT'S HOMEOPATHIC SPECIFICS Y J B B BD Y DDY 8 B F B F x F D > q q j 8 8 J 4 8 8 24 B j 88 4 4 4 8 q 8 bb B 6 B q B b b b B 4 B D J B B b B

More information

Chapter 6: Momentum Analysis

Chapter 6: Momentum Analysis 6-1 Introduction 6-2Newton s Law and Conservation of Momentum 6-3 Choosing a Control Volume 6-4 Forces Acting on a Control Volume 6-5Linear Momentum Equation 6-6 Angular Momentum 6-7 The Second Law of

More information

Worksheets for GCSE Mathematics. Algebraic Expressions. Mr Black 's Maths Resources for Teachers GCSE 1-9. Algebra

Worksheets for GCSE Mathematics. Algebraic Expressions. Mr Black 's Maths Resources for Teachers GCSE 1-9. Algebra Worksheets for GCSE Mathematics Algebraic Expressions Mr Black 's Maths Resources for Teachers GCSE 1-9 Algebra Algebraic Expressions Worksheets Contents Differentiated Independent Learning Worksheets

More information

Spherical orthogonal coordinate system (3 dimensions) Morio Kikuchi

Spherical orthogonal coordinate system (3 dimensions) Morio Kikuchi Spherical orthogonal coordinate system (3 dimensions) Morio Kikuchi Abstract: Product of metric coefficient and radius of round line is constant in spherical orthogonal coordinate system. Coordinates and

More information

Lecture 8 Analyzing the diffusion weighted signal. Room CSB 272 this week! Please install AFNI

Lecture 8 Analyzing the diffusion weighted signal. Room CSB 272 this week! Please install AFNI Lecture 8 Analyzing the diffusion weighted signal Room CSB 272 this week! Please install AFNI http://afni.nimh.nih.gov/afni/ Next lecture, DTI For this lecture, think in terms of a single voxel We re still

More information